How did the area of the rectangle change if its length and width were reduced by 10%?

The area of a rectangle, as you know, is calculated by the formula:

S = A x B,

where A is the length of the rectangle and B is its width.

If the length and width are reduced by 10%, then their new values will equal 0.9 x A and 0.9 x B. The new area will be equal to:

S₁ = 0.9 x A x 0.9 x B;

S₁ = 0.81 x A x B.

Now you can find how the area of the rectangle will change:

S₁ / S = 0.81 x A x B / A x B;

S₁ / S = 0.81.

Answer: when the length and width are reduced by 10%, the area of the new rectangle will decrease by 0.81 times.